Equivalence between domain walls and "noncommutative" two-sheeted spacetimes: Model-independent matter swapping between branes

We report a mathematical equivalence between certain models of the Universe relying on domain walls and noncommutative geometries. It is shown that a two-braneworld made of two domain walls can be seen as a "noncommutative" two-sheeted spacetime under certain assumptions. This equivalence also implies a model-independent phenomenology, which is presently studied. Matter swapping between the two branes (or sheets) is predicted through fermionic oscillations induced by magnetic vector potentials. This phenomenon, which might be experimentally studied, could reveal the existence of extra dimensions in a new and accessible way.